A model for the formation and propagation of faults from the coalescence of smaller-scale systems of cracks: Finite Element Method-based numerical approach

The 2D, plane strain, Finite Element Method-based linear elastic model that I present aims to assess the differential stress response to variations in the geometric configuration of a system of multiple collinear elliptic cracks intercepting a body of rock undergoing elastic deformation. The assumption underlying this simulation is that a collection of thin voids in a continuum medium can replicate the features observed in a system consisting of rough fault profiles in partial contact subjected to shear. The linear elastic model is designed to reproduce the stress and displacement fields around a rough fault, with a specific focus on stress concentration around its contact asperities. The model also allows to record the principal stress field on the domain for a wide range of scales and geometric properties of the system of collinear cracks embedded in the deforming rock. Analyzing the dependence of differential stress on parameters describing the geometry of rough fractures allows for considerations on the primary factors influencing brittle failure. Additionally, the examination of principal stresses around the tips of the cracks helps evaluate the potential orientation of new fracture patterns that may emerge when the yield strength of the deforming material is locally exceeded. The magnitude and orientation of the principal stresses are also crucial for the understanding of fracture coalescence and frictional reactivation of shear cracks in an elastic rock, which in turn is one of the main factors that govern the seismic cycle of natural faults. Furthermore, a comparison of the results of the present model with recent wing crack models of brittle creep suggest that our code may also be useful to obtain estimates of the critical distance between cracks for their interaction to coalesce into larger fractures. The process is assumed to indefinitely continue at greater scales, which offers the chance to propose a model for fault formation and propagation.